; ; ; "ActiveFedora::Aggregation::ListSource" . a , ; "Estimating Linear Filters With Errors in Variables Using the Hilbert Transform"; ; "batchuser@example.com"; "Hinich, Melvin J.", "Weber, Warren E."; "Federal Reserve Bank of Minneapolis"; "Errors-in-variables", "Hilbert transform", "Minimum phase-lag", "Linear filter", "Phase unwrapping"; "In this paper we present a consistent estimator for a linear filter (distributed lag) when the independent variable is subject to observational error. Unlike the standard errors-in-variables estimator which uses instrumental variables, our estimator works directly with observed data. It is based on the Hilbert transform relationship between the phase and the log gain of a minimum phase-lag linear filter. The results of using our method to estimate a known filter and to estimate the relationship between consumption and income demonstrate that the method performs quite well even when the noise-to-signal ratio for the observed independent variable is large. We also develop a criterion for determining whether an estimated phase function is minimum phase-lag."^^; "1992-08"; "2019-10-21T15:28:00.00377377+00:00"^^; "https://doi.org/10.21034/sr.96"; ; "https://creativecommons.org/licenses/by-nc/4.0/"; "Thu Nov 7 22:19:07 2019"; "https://creativecommons.org/licenses/by-nc/4.0/"; "Research Paper"; "342", "832"; "Staff report (Federal Reserve Bank of Minneapolis. Research Department)"; "096"; "Linear filter", "Hilbert transform", "Minimum phase-lag", "Phase unwrapping", "Errors-in-variables"; ; ; ; ; "Federal Reserve Bank of Minneapolis. Research Department"; "Published in: _Signal Processing_ (Vol. 37, No. 2, May 1994, pp. 215-228) https://doi.org/10.1016/0165-1684(94)90104-X. "^^; ; "Publication" . ; .